Skip to main content
Log in

Cyclic Theories

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

We describe a geometric theory classified by Connes-Consani’s epicylic topos and two related theories respectively classified by the cyclic topos and by the topos \([{\mathbb N}^{\ast }, \textbf {Set}]\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Caramello, O.: The unification of Mathematics via Topos Theory, arXiv: http://arxiv.org/abs/math.CT/1006.3930v1

  2. Caramello, O.: Extensions of flat functors and theories of presheaf type, arXiv: http://arxiv.org/abs/math.CT/1404.4610v1, to appear in a book for Oxford University Press provisionally entitled Lattices of theories (2015)

  3. Connes, A.: Cohomologie cyclique et foncteur E x t n. C.R. Acad. Sci. Paris, Sér. I Math. 296, 953–958 (1983)

    MathSciNet  MATH  Google Scholar 

  4. Connes, A., Consani, C.: Cyclic homology, Serre’s local factors and the λ-operations, arXiv: http://arxiv.org/abs/math.AG/1211.4239v1

  5. Connes, A., Consani, C.: Cyclic structures and the topos of simplicial sets. Journal of Pure and Applied Algebra 219(4), 1211–1235 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Connes, A., Consani, C.: Projective geometry in characteristic one and the epicyclic category, arXiv: http://arxiv.org/abs/math.AG/1309.0406v1

  7. Connes, A., Consani, C.: The Arithmetic Site, arXiv: http://arxiv.org/abs/math.NT/1405.4527v1

  8. Connes, A., Consani, C.: Geometry of the Arithmetic Site, arXiv: http://arxiv.org/abs/math.AG/1502.0558v1

  9. Connes, A., Consani, C.: The Cyclic and Epicyclic Sites, arXiv: http://arxiv.org/abs/math.AG/1407.3945v1

  10. Fuchs, L., Salce, L.: Modules over non-Noetherian domains, Mathematical Surveys and Monographs 84, American Mathematical Society (2001)

  11. Goodwillie, T.: Letter to F. Waldhausen (August 10, 1987)

  12. Moerdijk, I.: Cyclic sets as a classifying topos (Utrecht, 1996), available at http://ncatlab.org/nlab/files/MoerdijkCyclic.pdf

Download references

Acknowledgments

We warmly thank Alain Connes for useful discussions on the subject matter of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olivia Caramello.

Additional information

Supported by a CARMIN IHÉS-IHP post-doctoral position whilst writing this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Caramello, O., Wentzlaff, N. Cyclic Theories. Appl Categor Struct 25, 105–126 (2017). https://doi.org/10.1007/s10485-015-9414-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-015-9414-y

Keywords

Mathematics Subject Classification (2010)

Navigation